Question

For the shaded shape shown 1. Calculate the area of the shaded shape 2. Calculate the location of the x-centroid of the shaded shape 3. Calculate the location of the y-centroid of the shaded shape 4. Calculate the moment of inertia of the shaded shape about the y centroidal axis 5. Calculate the moment of inertia of the shaded shape about the x centroidal axis 6. Calculate the moment of inertia about the x axis (along the bottom of the shape) 7. Calculate the moment of inertia about the y axis (along the left edge of the shape) 8. Calculate the polar moment of inertia about the origin (lower left corner of the shape)

> Hi pls answer this to my Problem, ty

Answer 1

Area of the shaded shapdA)= Ai + A 2-A3 A = (4x10) + (5x5x80) – ( 432 A = 40 +25 - 12.566 - A= 52.434 in? Re-centroid; &i= 10 -5";; Rg= Bat *$0 3 3.333.23 = 4". AIR, + A2X2 - A383 (40*5)+(25x3.333) -(12.566*4) Ait A2 -A3 52.434 a = 4.445"

© Y-contoroid: 9, = 4"2"., 4, = 3+(5x5) = 4.667; Yg= 3". T Ary, + Azyz - Azyz (40x2)+(25x4669) (12.566x3) 52.434 AiA2-A3 1% = 3.032". BHA + - oy 36 64 २ By using parallel arris theorem, Iyy = BO PA A m2 + Ah? - Chaptet a 13) - 10 xust (4x0X 5–4.415) + 60x63*+ (4x10x)(4-445-4X) -("X1924 (+*4.445-439) 36 - 64 = 65.654 + 65.636 - 3727415.055 12 SXIC EX Inz - De2+ Alt + helt ani - cena net A hip) = 40°t (4*( 3.02-* + 5xl5° +(6x05)(Ex543 – 3.082) - (harmony + (147) 3.022-333) 36 12 11 x(2)4 + 64 = 375.934 + 205.790 - 049 12.579. Ira 11 © 164 Ixx - Bp + Ami + Bx3 + Ab-(Tox + Abs). 1999+(480(2)*+ 10x15)*7 (3x10x5)(8+633) .125.660 = 213.333 + 579.244 – 191 A46958 in 666.917

O 12 12 36 IME = Dipe +Anitt + Ab} - ( noun + A be) - 4X10° + (4%)) + 5x10° + (x10x{}xio)? - (x4y + x4433) = 1333.333, + 416-611 – 213.622 try = 1536.322 in 4, z' aseis. olis Polas mement of InestidJ means its about which is perpendicular to X & Y.@ origin. So by using perpendicular as is theorem, J- (I x + ( Irpa JE SC666.99]+ (1536.322) 2 J = 1674.832 in 47 All the 'b' values are the distance between the objects axis to the Ascis for which we are determining Moment of Inertia .
If you are aware of PARALLEL AXIS THEOREM AND PERPENDICULAR AXIS THEOREM it's easy to do this type of problems